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Issue 3.08

The Astrophysics Spectator

April 26, 2006

This fortnight The Astrophysics Spectator digresses from black holes to discuss the mechanism that produces black holes: the instability that causes stars to collapse to black holes. Two new pages on stellar collapse have been placed on the “Stars” topical path.

Planets don't collapse, but stars often do. The reason is that special relativity comes into play for large stars, and this destabilizes the star.

At the core of a planet like Saturn, the pressure is provided by cold electrons. Two principles of quantum mechanics is that the electrons can have very specific energies starting at zero energy and increase by finite increments, and the only two electrons can simultaneously have the same energy. When the electrons are cold, they occupy all of the lowest energy levels. This means that for the cold material at the center of Saturn, most of the electrons have energy that they cannot lose, because they can only lose energy by dropping to a lower energy state, and all of the lower energy states are occupied by other electrons. The pressure of these energetic electrons on their surroundings is called degeneracy pressure, and it acts not only at the core of cold planets like Saturn, but at the center of degenerate dwarf stars, the remains of small stars that have consumed their nuclear fuel.

At the core of Saturn, the most energetic electrons have velocities that are far below the speed of light. A consequence of this is that the force of the degeneracy pressure in Saturn is in a stable equilibrium against the force of gravity. If we could squeeze Saturn to a slightly smaller radius, we would see the force from the degeneracy pressure increase faster than the force of gravity, which would cause Saturn to expand back to its equilibrium radius.

However, if the mass of a cold object is large enough, the pressure at the object's core becomes so high that the electrons in the highest energy levels move at close to the speed of light. This effect causes a catastrophe, because now a slight squeeze of the body from equilibrium causes the force of the pressure to rise at the same rate as the force of gravity. The body will not expand back to its equilibrium radius, but will instead continue to collapse into something smaller.

This whole process of an object becoming unstable when the particles at the core start moving at speeds close to the speed of light is not confined to objects supported by electron degeneracy pressure. Neutron stars, which are supported by neutron and proton degeneracy pressure, collapse when the neutrons and protons move at relativistic velocities. A very high temperature gas can have particles moving at near the speed of light, and a gas dominated by photon pressure is supported by photons moving at the speed of light, and both are unstable to gravitational collapse in the absence of thermonuclear fusion. The consequence is that once a very massive star converts all of its nuclear fuel to iron, it becomes unstable and rapidly collapses.

This link between special relativity and stellar collapse suggests that the degenerate dwarf and neutron star each have a maximum mass. Degenerate dwarfs are no larger than about 1 and a half solar masses, while neutron stars are no larger than about 2 and a half solar masses. While theorists have hypothesized the existence of stars similar to neutron stars but composes of more exotic material, these also are limited in mass to a few solar masses. This natural tendency to instability of compact stars is the reason we believe that the core collapse of a very large star produces a black hole rather than a neutron star.

Next Issue: The next issue of The Astrophysics Spectator is scheduled for publication on May 9.

Jim Brainerd


The Gravitational Collapse of Stars. A star that has exhausted its nuclear fuel can become unstable and collapse to a neutron star or a black hole. This instability, where gravity overwhelms the pressure at the core of a star, is primarily a consequence of special relativity; when the particles in the core move at much less than the speed of light, the star is stable, but when the particles move at close to the speed of light, the star is unstable. This effect sets a maximum mass for some types of star. (continue)

The Instability of Compact Stars. Once a star ends it life of active fusion, it collapses into one of three types of object—a degenerate dwarf, a neutron star, or a black hole. Which of these three is selected depends on the size of the star. Very small stars become degenerate dwarfs, stars somewhat larger than the Sun become neutron stars, and very large stars become black holes. These paths are the inevitable consequence of the inherent gravitational instability of large degenerate dwarfs and neutron stars. (continue)

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